Solve (5a^{3}b^{5})(-5b^3c^3)(a^3c^4)

$$( 5 a ^ { 3 } b ^ { 5 } ) ( - 5 b ^ { 3 } c ^ { 3 } ) ( a ^ { 3 } c ^ { 4 } )$$

Evaluate

$$-25a^{6}c^{7}b^{8}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 3 and 3 to get 6.

$$5a^{6}b^{5}\left(-5\right)b^{3}c^{3}c^{4}$$

To multiply powers of the same base, add their exponents. Add 5 and 3 to get 8.

$$5a^{6}b^{8}\left(-5\right)c^{3}c^{4}$$

To multiply powers of the same base, add their exponents. Add 3 and 4 to get 7.

$$5a^{6}b^{8}\left(-5\right)c^{7}$$

Multiply 5 and -5 to get -25.

$$-25a^{6}b^{8}c^{7}$$

Differentiate w.r.t. a

$$-150a^{5}c^{7}b^{8}$$